While reading a generator AVR operation description: "When a transformer is used to boost the generator voltage, the transformer impedance provides the DROOP characteristic (voltage drop) and so compensates for any reactive cross current flow. In these circumstances, the AVR does not provide a DROOP characteristic".
AVR of generator has a circuitry which senses reactive component & hence called quadrature droop compensation. When we operate multiple generators in parallel excitation /voltage droop of each generator contributes to reactive power sharing accordingly. Hence for ensuring proportional reactive power sharing quadrature droop of AVR is set accordingly. Transformer voltage drop is proportional to KVA & not Kvar. If the % impedances of the all generator transformers are equal very low droop can be adjusted on AVR. Secondly whenever automatic Active & Reactive load sharing systems are provided, a master voltage controller & master frequency controller is always provided which corrects the terminal /Bus voltage & frequency drop due to AVR & Governor droop. This means if master voltage controller & master frequency controller is provided transformer & generator voltage drop & droop effect is compensated.
What the description is attempting to explain is that if a transformer is between the genset and the load a voltage droop will take place from no load to full load. This is due to the impedance of the transformer. As an example let's say you have a 480V 3 phase genset, and a 480V/208-120V delta wye step down transformer with 5% impedance. At no load and assuming the transformer input is 480V the output will be very close to 208-120V. At full load and assuming the genset is setup to hold output voltage at 480V, the transformer secondary will now be at 197.5-114V. The generator AVR operation is actually independent of whether or not you have an output transformer in the system. Also a AVR droop is not a requirement. There are plenty of operating modes that do not rely on a droop style control in the genset. Many generators which are used for peak shaving do not employ a drooping AVR but instead hold a fixed PF. Droop AVRs can be used in an islanded situation.
Finally as an option, if you have an output transformer with suitable impedance you can choose to set the AVR to non-drooping, even on an isolated bus with other gensets set up similarly. If the gensets have offset voltages between their terminals, which is common, a current will flow between them. The current will lead to a voltage drop across the output transformers and the system will be satisfied. The impedance of the transformer and the difference in voltages between the gensets will dictate how much current flows. Generally this is not my preferred method as it is a fairly crude method to achieve the end, however if there are few alternatives, it can be done.